Question

What is the range of the function `sqrt(16-x^4)`?

Answer 1

See below.

Explanation:

The minimum value `(16 - x^4)` is `0` for real numbers.

Since `x^4` is always positive maximum value of radicand is `16`

If including both positive and negative outputs the range is:

`[ -4 , 4 ]`

For positive output `[ 0 , 4 ]`
For negative output `[ -4 , 0 ]`

Theoretically '`f(x) = sqrt( 16- x^4)` is only a function for either positive or negative outputs, not for both.i.e:

`f(x) = +- sqrt(16 - x^4 )` is not a function.